NASHVILLE, Tenn. — Four same-sex couples are asking a federal judge for a preliminary injunction that would force Tennessee to recognize their marriages.

The couples filed a suit in U.S. District Court in Nashville last month challenging Tennessee laws that prohibit recognition of same-sex marriages. They claim in court filings that the laws violate constitutional guarantees of equal protection and due process.

The request for the injunction would apply only to the four couples who are plaintiffs in the lawsuit. If approved, it would be in effect while their case works its way through the courts.

The couples, who include a full-time Army reservist and his husband and two professors of veterinary medicine, all formerly lived and married in other states and later moved to Tennessee to pursue careers and make new homes for their families.

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The lawsuit argues that Tennessee’s laws prohibiting recognition of the couples’ marriages violates the U.S. Constitution’s guarantee of equal protection and due process and the constitutionally protected right to travel between and move to other states.

A spokeswoman for the state attorney general’s office said in an email that attorneys there are reviewing the filing and are prepared to defend Tennessee law and the state constitution.